Yes it will work, running a PCIe 3.0 card on a x16 PCIe slot will not show any difference in performance, maybe ~1fps, but it is definitely not noticable. If you plan on running two hd7870's then you may see a difference of a few fps when running on a PCIe 2.0 slot, however even then it is not that big of a deal. So a hd7870 will run fine on your PCIe 2.0 motherboard, I checked and you have a Pcie X16 2.0 slot on your motherboard, so you are good to go!